A few much belated comments
follow these quoted posts:
On Feb 4, 2007, at 2:33 AM, Sandra wrote:
(1) If the bias of the IV estimates cause them to
approach the (inconsistent) OLS estimates (which
are significantly positive), then if I get larger
IV estimates (compared to the OLS estimates) does
that mean my estimates would be even larger if I
had strong instruments? In other words, would
that imply my IV estimates are biased downward?
(2) I read a review by Stock and co-authors, and
they mention that if I estimate my equation using
liml, then my results will be more robust to weak
instruments, further, I noticed that the
Stock-Yogo critical values are much lower, when I
use LIML. Am I making a correct intepretation of
their text?
(3) In the review by Stock and co-authors, they
mention that the rule of thumb is that an F-test
should be greater than 10. They also mention in
the context of multiple instrumental variables
the Cragg-Donald F statistic and the Stock-Yogo
critical values. Does this Cragg-Donald
statistic also work in a one instrument context?
This is because, when I look at this statistic my
instruments seem to be higher than the 10%
Stock-Yogo critical value. If each of these
statistics work as a sufficient condition (rather
than a necessary condition) for having strong
instruments, then I would rather report the
Cragg-Donald statistic, considering this is
statistically sound.
My problem is that it is very tough to get
exogenous instruments for my variable, and this
is the only instrument I have managed to come up
with, so I would like to stick to it, if at all
possible.
On 2/4/07, at 9:00 AM, Kit Baum <baum@bc.edu> wrote:
(1) That sounds sensible.
(2) As I understand it the distribution of the
S-Y critical values differ depending on, among
other things, the underlying estimator. So I
would not make much of the fact that the CVs
differ between IV-GMM and LIML.
(3) In the context of a single FSR, the notion
that the ANOVA F should exceed 10 is a rule of
thumb suggesting that the FSR is reasonably
strong. The first example in ivreg2 help shows a
model with a single endogenous regressor for
which F = 13.79 (zero pvalue). The Anderson
canon. corr. LR stat. is 54, with a pvalue of 0,
ad the Cragg-Donald min eigenvalue stat is 56,
with a pvalue of zero. The null for each of
these tests is underidentification, with
rejection indicating that the model is
identified. The latest version of ivreg2 (soon
to be released) reformats these results to make
the underlying hypotheses clear. However that
same model has a significant Sargan test
statistic, suggesting that the overidentifying
restrictions are soundly rejected by the data.
This implies that the instruments are inadequate
and must be replaced. So you can have
sufficiently strong instruments but still fail
the Sargan (or Hansen J, in IV-GMM) test. I
would worry about that in your model.
Now my comments:
(1) It may sound sensible, but it ain't
necessarily so. With weak instruments, you can
get some quite wacky estimates, and remember
also that the variance of your IV estimate is
high in part because you have weaker instruments
than you would like. If you had a very good
instrument, you could expect to see the variance
of your second stage estimate drop, and the
point estimate to change--whether the point
estimate would go up or down is impossible to
predict.
(2) The S-Y critical values are for the "vanilla"
linear IV only, and should be used only as rules
of thumb--remember that the measures of
the predictive quality of the first stage might
on average result in your bias being 5% of the
OLS bias--but your mileage may vary!
(3) I agree with Kit's concern about the results
of an overid test. On your original question
(3), none of the available tests are sufficient
to conclude with certainty that you don't have
weak instruments. Stock and Yogo
(http://www.nber.org/papers/t0284) indicate
(p58) that the min eigenvalue of the CDstat when
you have one endogenous regressor and three
excluded instruments should be greater than
13.91 to reduce bias to 5% of the OLS bias in
simulations. This does not say what the bias of
your particular IV application is, but can serve
to reassure readers if your first-stage F is 22.
(4) In her first post, Sandra asks "if stata
contains any routine that would provide
estimates robust to weak instruments." I
believe she means "can Stata provide tests of
correct size in the presence of weak
instruments?" and the answer is yes, for the case
of a single endogenous regressor--just type
net describe condivreg, from(http://www.stata.com/users/bpoi)
and install the program, which follows the implementation of
Anna Mikusheva (Harvard University) and Brian P. Poi (StataCorp LP)
"Tests and confidence sets with correct size when the instruments are
potentially weak." Stata Journal 6(3).
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